Question

Two homogeneous spheres $A$ and $B$ of masses $m$ and $2m$ having radii $2a$ and $a$ respectively are placed in touch. The distance of the centre of mass from the centre of the first sphere is

• A. $a$
• B. $2a$
• C. $3a$
• D. none of these

Answer 1

Answer: (B)

We assume that origin is situated at $O_{1}$ .

$\therefore x_{1}=0$ , $m_{1}=m$
$x_{2}=3a$ , $m_{2}=2m$
$\therefore x_{cm}=\frac{m_{1} x_{1} + m_{2} x_{2}}{m_{1} + m_{2}}$
$=\frac{\left(m \times 0\right) + \left(2 m \times 3 a\right)}{m + 2 m}$
$=\frac{6 ma}{3 m}=2a$